L2-regularization based two-way weighted neutrosophic clustering with Manhattan and Euclidean distances

Neutrosophic c-means clustering (NCM) is a promising algorithm to solve uncertainty and imprecision in data analysis. Despite its intensive exploration, one major challenge still needs to be addressed, i.e. how to efficiently reveal the latent structure of the dataset and improve clustering performance by discriminating the contributions of different objects and features in the clustering process. In this paper, a general neutrosophic clustering framework is proposed to address the aforementioned issue. Specifically, we develop an $L_2$-regularization based two-way weighted scheme to learn the discriminative capability of different features and gauge the importance of different objects. In the proposed framework, we employ Manhattan and Euclidean distances as two different dissimilarity metrics, respectively. Additionally, we design the iterative optimization procedures to obtain neutrosophic partition, cluster centers, object weights and feature weights. Extensive experimental studies corroborate that the proposed algorithms achieve superior performance over other comparative algorithms on five synthetic and twenty real-world datasets.